Numerical simulations were performed to investigate the effects of drop freezing in immersion and contact modes for a convective situation. For the description of heterogeneous drop freezing, new approaches were used considering the significantly different ice nucleating efficiencies of various ice nuclei. An air parcel model with a sectional two-dimensional description of the cloud microphysics was employed. Sensitivity studies were undertaken by varying the insoluble particle types as well as the soluble fraction of the aerosol particles showing the effects of these parameters on drop freezing and their possible impact on the vertical cloud dynamics. The soluble fraction $varepsilon$ decides whether immersion or contact freezing will be the major process. For high $varepsilon$ values, immersion freezing is the dominant process. In such cases the freezing process is strongly temperature-dependent, and the ice nucleation efficiency of the insoluble particle types becomes important for efficient freezing. The freezing point depression can be neglected because of the preferential freezing of large drops. Contact freezing is the major process in cases of lower $varepsilon$ values. In these cases the freezing process is less dependent on temperature and aerosol particle type. For conditions of efficient freezing, cold, high-altitude, completely glaciated clouds could form. The presented approaches for immersion and contact freezing can be incorporated further into mesoscale and global models to estimate the effects of specific ice nuclei on ice formation.